cosine lobe based relighting from gradient illumination … · 2009. 5. 6. · cosine lobe based...

Cosine Lobe Based Relighting from Gradient Illumination Photographs

Graham Fyffe∗

University of Southern California Institute for Creative Technologies

Figure 1: Relighting from four photographs: Cosine lobes are fit to the reflectance function at each pixel and then relit with a point light.Left: uniform and gradient illumination input photographs; Right: relit images under some example point light illumination conditions.

1 Introduction

Image-based relighting is a powerful technique for synthesizing im-ages of a scene under novel illumination conditions, based on a setof input photographs. While successful relighting methods exist,they either require many photographs [Debevec et al. 2000], or op-erate on a limited class of materials or illumination conditions [Maet al. 2007][Ramamoorthi 2006].

We present an image-based method for relighting a scene by an-alytically fitting a cosine lobe to the reflectance function at eachpixel, based on gradient illumination photographs. An acceptablefit can be obtained for many materials using a single, colored co-sine lobe, which is obtained from just two color photographs: oneunder uniform white illumination and the other under colored gra-dient illumination. For materials exhibiting wavelength-dependentscattering distributions, a better fit can be obtained using an inde-pendent cosine lobe for each of the red, green, and blue channels,which is obtained from three monochromatic gradient illuminationconditions instead of a single colored gradient condition, requiringa total of four photographs.

2 Method

We photograph the scene inside a geodesic sphere of colored LEDlights, which can be programmed to produce gradient illuminationas well as uniform white illumination, similar to [Ma et al. 2007].We compute the mean spherical angle of reflected light α from theratio images of the gradient illumination photographs to the uni-form illumination photograph, and we compute the total amount ofreflected light I from the uniform illumination photograph, as in[Ma et al. 2007]. If a single colored gradient is used instead of sep-arate x, y and z gradients, we make the assumption that the ratioimages are wavelength-independent. Unlike [Ma et al. 2007], wedo not estimate normals or albedo from these quantities, but insteadtake them as measured properties of the reflectance function itself.Further, we make use of the additional information contained withinthe denominator in the normalization step of computing the meanspherical angle. This allows us to solve for an additional parameter

∗e-mail: fyffe@ict.usc.edu

in the reflectance function, which in our case is the exponent n of acosine lobe reflectance function.

We explore two different cosine lobe reflectance functions, whichintegrate easily over the uniform and gradient illumination condi-tions, so that an analytic solution for the fit is obtained. Cosinelobes of the form kmax(0, α · l)n with k = 1

2πI(n + 1) work

well for diffuse and specular materials, but fail for materials withbroader scattering such as fur. An alternative form k( 1

2α · l + 1

2)n

with k = 14πI(n+ 1) works well for broad scattering and still pro-

duces visually plausible results for diffuse and specular materials.

3 Results

The method works well whenever the reflectance function is wellapproximated by a single smooth lobe. Results for highly specularmaterials are noisy, due to the hardware limitation of using LEDlights to approximate continuous illumination. Ground truth com-parisons confirm that effects due to non-smooth reflectance func-tions are not reproduced, such as hard shadows, but even with theselimitations the method produces visually plausible results with nodisturbing artifacts over a wide range of materials and illumination.Furthermore, the results are more consistent with ground truth thanthose obtained from using the input photographs as a linear basis.

References

DEBEVEC, P., HAWKINS, T., TCHOU, C., DUIKER, H.-P.,SAROKIN, W., AND SAGAR, M. 2000. Acquiring the re-flectance field of a human face. In Siggraph 2000, ComputerGraphics Proceedings, ACM Press / ACM SIGGRAPH / Addi-son Wesley Longman, K. Akeley, Ed., 145–156.

MA, W.-C., HAWKINS, T., PEERS, P., CHABERT, C.-F., WEISS,M., AND DEBEVEC, P. 2007. Rapid acquisition of specular anddiffuse normal maps from polarized spherical gradient illumina-tion. In Rendering Techniques, 183–194.

RAMAMOORTHI, R. 2006. Modeling Illumination Variation withSpherical Harmonics. In Face Processing: Advanced ModelingMethods. 385–424.